Nearly 20 years since I last worked there, but there is some climbing on poor quality limestone along the escarpment to the west of Riyadh near the prominent pinnacle known as 'Faisals Finger / Pinnacle'. There is more a little further west in the area known as Hidden Valley -- both can be found on Google Earth. Whilst the escarpment and cliffs look impressive the rock is anything but!

I've also climbed on some good granite that is located some 200km west of Riyadh along Highways 40 and 50 ( old and new Makkah roads)

I've heard tales of good climbing on Igneous rock in the Taif area - but have never been there.

Issues you may encounter is that you will inevitably have to pass through checkpoints to visit these locations. A 'letter of travel' from your employer / sponsor that has been stamped by the interior ministry is virtually essential.

The further you get from the major cities, the more you get in to very traditional tribal areas. Some encounters with locals have been fascinating - others downright scary!

I was lucky as my sponsor's brother was deputy justice minister, and seeing the family name on my documents kept me out of a number of embarrassing situations on my lone wanderings that might have otherwise resulted in at least a night in jail!